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How to Design Mechanisms and Linkages Using CAD (Step-by-Step Guide)

How to Design Mechanisms and Linkages Using CAD (Step-by-Step Guide)

Introduction to Linkages and Mechanisms

A linkage is a mechanical system made up of links connected together by joints. The links are rigid bodies and the joints allow relative motion between the links. When linkages are connected together to perform a task, they form a mechanism.

Linkages and mechanisms are essential components in machinery and mechanical devices. They are used to transform motion, forces, and energy in controlled ways to accomplish useful functions. Common applications include:

  • Pumps, motors, and engines - Pistons, crankshafts, cams, and valve trains are linkage mechanisms that convert between rotary and linear motion.

  • Robotic arms and manipulators - Jointed linkages allow a robotic arm to move and position tools. Grippers at the end effector can pick up objects.

  • Foldable structures - Scissor linkages and pantographs allow structures to expand and collapse. Examples include folding car roofs and expandable antennas.

  • Transportation systems - Linkages in suspension systems, landing gear, and folding wings allow controlled motion on planes, trains, and automobiles.

  • Manufacturing machinery - Linkages transfer motion for tasks like stamping, pressing, lifting, feeding, and assembly.

The versatility of linkages allows mechanical engineers to design systems ranging from precision medical devices to heavy machinery. By selecting and configuring different linkage types, nearly any desired motion or force transmission can be achieved. This makes linkage design an indispensable engineering skill for creating mechanized solutions to real-world problems.

Joints for Linkage Construction

Mechanical linkages are made up of links connected together by joints. The joints provide a constrained relative motion between the links. There are several basic types of joints used in linkage design:

Revolute Joint

  • Allows rotation about the joint axis

  • Provides a single rotational degree of freedom

  • Also called a hinge joint

  • Used in door hinges, 4-bar linkages, etc.

Prismatic Joint

  • Allows linear sliding motion along the joint axis

  • Provides a single translational degree of freedom

  • Also called a slider joint

  • Used in automobile suspensions, machine tools, etc.

Cylindrical Joint

  • Combines properties of a revolute and prismatic joint

  • Allows both rotational and translational motion

  • Provides two degrees of freedom

  • Used in robot arms, universal joints, etc.

Ball and Socket Joint

  • Allows rotation in all directions, 3 rotational degrees of freedom

  • Used in hip and shoulder joints, vehicle tie rods, etc.

Universal Joint

  • A coupled pair of hinges with intersecting axes

  • Allows two degrees of rotational freedom

  • Used in driveshafts, control rods, etc.

Planar Joint

  • Constrains relative motion to a plane

  • Often consists of a slider combined with a hinge

  • Provides two translational and one rotational degrees of freedom

The choice of joints significantly impacts the mobility, function, and analysis of a linkage mechanism. Selecting appropriate joint types is a key step in designing robust and useful linkages.

2-Bar Linkages: Triggers

The 2-bar linkage is the simplest linkage, consisting of two links connected by a single joint. 2-bar linkages are commonly used as triggers to control the release of a mechanism through the relative motion of the links.

The joint in a 2-bar linkage is usually a revolute or prismatic joint. When one link is pulled or turned, it causes the connected link to move correspondingly. This allows 2-bar linkages to function as switches or latches that trigger other motions.

For example, a door latch consists of a 2-bar linkage. When the door handle is rotated, it moves one link which pulls on the second link connected to the latch, releasing it and allowing the door to open. The trigger action comes from the kinematic relationship between the rotating and translating motions of the two links.

Other common examples employing 2-bar linkages as triggers include toggle clamps, bell cranks, snap action switches, spring loaded pins, and hydraulic valve actuators. The toggling or snap action provides a distinct trigger point as one link hits a stop, rapidly switching the position of the second link.

So despite their mechanical simplicity, 2-bar linkages play an important role as triggers for activating and releasing mechanisms across many applications and industries. Their basic but reliable functionality makes them a key component in mechanisms where a trigger action is required.

4-Bar Linkages

4-bar linkages are the most commonly used type of planar linkage mechanism. They consist of four links connected by four revolute joints to form a closed loop. The links are called the ground link, input link, coupler link, and output link.

4-bar linkages are used for a wide variety of tasks including:

  • Rocker arms - Used to convert rotational motion into reciprocating motion, often seen in internal combustion engines. The downward movement of the piston is converted into rotational motion of the crankshaft.

  • Pantographs - Used to create an extended range of movement while keeping parts in sync. Often used for extending the reach of high voltage lines or creating a larger movement for a smaller input.

  • Straight line mechanisms - Used to convert rotational motion into approximate straight line motion. The Watt's linkage and Peaucellier–Lipkin linkage are examples that generate near-perfect straight line motion from a rotational input.

The versatility of 4-bar linkages arises from the ability to carefully design the link lengths and pivot points to achieve desired input-output characteristics. By tuning these parameters, 4-bar linkages can generate complex non-linear output motions from a simple rotational input. This makes them an indispensable tool for mechanical engineers and product designers.

Kinematic Synthesis of 4-Bar Linkages

One of the most powerful aspects of 4-bar linkages is that they can be designed to have very specific output characteristics. This process is known as kinematic synthesis. The goal is to design the dimensions of the 4 linkage bars such that the coupler curve, or the trajectory traced by the coupler point, has the desired shape and motion.

There are two main methods for synthesizing 4-bar linkages - the precision point method and graphical synthesis.

Precision Point Method

In the precision point method, you specify 3 precise points that you want the coupler curve to pass through. The relative positions of these 3 points will determine the general shape of the curve. By strategically picking the points, you can achieve straight line motion, approximate arcs and circles, or complex custom curves.

Once you've chosen the 3 points, the precision point method uses the mathematical constraints between the linkage parameters to numerically solve for all the unknown dimensions. This can be done by hand using algebra or programmed into CAD software to perform the calculations.

The key steps are:

1. Choose 3 precision points for the coupler curve to pass through

2. Write loop closure equations for the linkage at each precision point

3. Solve the simultaneous equations to find the linkage dimensions

4. Refine the dimensions and test in CAD until the curve passes through the points

The more intricate the curve shape, the more difficult it is to find a valid solution. But the precision point method enables designing very customized 4-bar motions.

Graphical Synthesis

Graphical synthesis involves manually sketching and tweaking 4-bar linkage designs until you achieve the desired coupler curve. It is more intuitive but less precise than the precision point method.

The steps involve:

1. Sketch an initial 4-bar linkage with estimated dimensions

2. Use drafting tools to draw the coupler curve

3. Modify the dimensions and redraw the curve until it matches the desired shape

4. Finalize the exact linkage proportions in CAD

Graphical synthesis requires visualizing how tweaking each linkage parameter affects the curve. It may take many iterations to converge on an optimal design. This method lends itself well to quick iteration in CAD, where you can rapidly visualize and simulate the effects of dimensional changes.

Both precision point and graphical techniques are important skills for designing 4-bar linkages with precisely tailored motions. Mastering kinematic synthesis enables creating linkages for a huge range of applications across industries.

Instant Centers and Linkage Analysis

Instant centers, also known as virtual centers, are imaginary pivot points located at the points where two links of a linkage would theoretically intersect if they continued along their lines of motion. Though the links do not actually intersect, the instant center provides a fixed pivot point that the links rotate about relative to one another.

Instant centers are useful in analyzing the movement of a linkage. By locating the instant centers between each pair of links in a mechanism, the angular velocity and angular acceleration between the links can be determined. Here's how it works:

  • Draw lines extending along the links of the mechanism to locate the instant center between a pair of links

  • The angular velocity of the two links will be equal at the instant center

  • As you move away from the instant center along the links, the angular velocities will differ based on the ratio of the distances from the instant center

  • The ratio of the distances provides the velocity ratio, which is used along with the input velocity to find the output velocity

  • A similar approach using the ratios of the accelerations and distances from the instant centers can be used to determine the output accelerations

Instant centers provide a powerful graphical tool for analyzing the kinematics of a linkage. By leveraging the velocity and acceleration ratios based on the locations of instant centers, the motion characteristics of a linkage can be fully defined. This method avoids complex algebraic calculations.

With CAD software, determining instant centers is made even easier. The software can calculate and display instant centers automatically based on a linkage design. The centers can even be animated to see how the pivot points move as the linkage operates. This provides further insight into the linkage's motion.

Understanding and utilizing instant centers is an important skill for effectively analyzing, optimizing, and animating linkage mechanism designs. Mastering this technique allows for creating high-performance linkages to suit any required specifications.

5-Bar and Multi-Bar Linkages

5-bar linkages contain 5 links connected by 5 revolute joints. The additional link provides one more degree of freedom compared to 4-bar linkages. This allows 5-bar linkages to trace more complex coupler curves.

Some applications of 5-bar linkages include:

  • Automobile windshield wipers - The extra link allows the wiper blade to follow the curve of the windshield more closely.

  • Printing presses - The 5-bar linkage converts rotary motion to near straight-line motion to move the presses back and forth.

Complex linkages can also contain 6 or more links connected in series. These multi-bar linkages can generate intricate motions and paths. They are useful for tasks that require precise coordination of multiple simultaneous movements.

Multi-bar linkages see heavy use in robotics and automation. For example, a robot arm contains a series of linked sections that must all move in a coordinated way to manipulate objects. Multi-bar linkages allow smooth and precise control over the robotic appendages.

Other applications of complex multi-bar linkages include loom weaving machines, clock escapements, and aircraft landing gear retraction systems. Advanced analysis methods like loop equations or matrix methods are needed to fully characterize their motion and design them to match functional requirements.

Scissor Linkages

Scissor linkages are constructed from two crossing links connected with a revolute joint at each end. This forms a linkage that can extend and retract, with the crossed links resembling the opening and closing motion of scissors. Scissor linkages provide the capability for large linear displacement from a compact folded configuration.

The crossed links in a scissor linkage are able to extend significantly longer than their individual link lengths when fully opened. In the fully closed configuration, the linkage compacts down to a fraction of its fully extended size. This allows scissor linkages to provide expansive motion from a condensed folded state.

Some key advantages of scissor linkages:

  • Large expansion ratio from compact storage size

  • Simple construction from two crossed links and four revolute joints

  • No sliding or rotating joints required

  • Extends in a straight line motion

Scissor linkages are commonly used in applications where a long linear extension motion is needed from a small retracted configuration. Some examples include:

  • Scissor lifts: Mobile platforms used to lift people or material vertically in a straight line using crossed scissor linkages. Allows reaching considerable heights from a low profile platform.

  • Foldable structures: Scissor linkages used in folding structures like expandable tables, retractable utility trailers, collapsible stages, and portable shelters need to maximize compact storage size.

  • Robotics: Scissor linkages provide linear extension for robotic arms or legs needing to reach and retract quickly.

The crossed pattern of scissor linkages makes them naturally well-suited for linear extension motions needing high expansion ratios from a condensed start position. Their simple construction also makes them a versatile building block for many expandable structures and mechanisms.

Compliant Mechanisms

Compliant mechanisms gain mobility from the flexibility and deformation of their components rather than just rigid links and joints. They are made of flexible materials that bend, flex, or distort under applied loads to achieve the desired motions. Compliant mechanisms utilize elastic deformation to transfer motion, force, or energy.

The main advantages of compliant mechanisms are:

  • No assembly required since they are monolithic and manufactured in one piece. This reduces costs.

  • No wear or need for lubrication at joints since there are no pin joints. This improves durability.

  • Reduced backlash or slack since there are no clearances between components. This increases precision.

Some applications of compliant mechanisms include:

  • MEMS - Microelectromechanical systems use compliant mechanisms on the microscale for switches, valves, positioners, and accelerometers. MEMS take advantage of the flexibility of microscale materials.

  • Robotics - Compliant joints and elements for lightweight robotics to softly interact with humans and the environment. Used in grippers, passive wrists, and spring-loaded legs.

  • Prosthetics - Artificial knee and ankle joints using flexible components to store and release energy when walking. Provides more natural motion.

  • Aerospace - Deployable space structures like solar arrays and antennas that unfurl using stored elastic energy. Allows compact stowage and reliable deployment.

Compliant mechanisms achieve flexibility through careful design and material choices rather than discrete joints. This allows smooth motion and impact mitigation. With thoughtful design, compliant mechanisms can achieve complex mechanical functions in simplified, lightweight, and compact packages.

Designing Linkages in CAD

CAD software provides a powerful tool to design, simulate, and optimize linkages and mechanisms. Here is a step-by-step process to design linkages from scratch in CAD:

1. Model the Links

  • Start by sketching the profile of each link in 2D. The links can be any shape - circular, rectangular, irregular, etc.

  • Extrude the 2D sketches into 3D solid bodies. Make sure to define the correct thickness in the extrusion

  • Apply any necessary features like fillets, chamfers, holes, etc. to the 3D links.

2. Add Joints

  • Add joints between the links to connect them. Revolute joints allow rotational motion between two components.

  • Joints can be added by mate connectors like axis lines or mate references. Define the type of mate for the desired joint motion.

  • Use width, angle, and alignment mates to properly locate the joints.

3. Apply Motion

  • Apply a motor to drive one of the links to animate the mechanism.

  • The motor can drive a revolute mate to produce rotational motion.

  • Adjust the motor properties like speed, torque, power, etc. as needed.

  • Add displacement drivers to other joints to serve as inputs.

4. Analyze and Validate

  • Use motion analysis tools to study the linkage as it moves through the range of motion.

  • The analysis can reveal problems like binding, overextension, undesired collisions, etc.

  • Iterate the design by adjusting link lengths, joint types, and motor settings to improve performance.

5. Additional Tips

  • Start simple - test basic concepts with simple 2-bar and 4-bar linkages before increasing complexity.

  • Use mate connectors instead of rigid joints when possible for more flexibility.

  • Create subassemblies of link clusters to improve organization and modularity.

  • Use length, angle, and curve dimensional constraints to optimize proportions.

  • Animate the linkage slowly section-by-section to thoroughly validate function.

By following this structured approach, you can turn imaginative linkage concepts into testable CAD models. The virtual design environment empowers you to efficiently try out ideas and refine mechanisms for optimal function.


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